first VPN will only allow you to connect to your own company network. Would be the same as connection to WiFi while in the same building. VPN is used for when you are away from the location but still want to connect to the offices network.
VPN is not going to be the most convenient thing to use as it won't stay connected all the time. You will find yourself needing to frequently go into settings, tell VPN to connect and then enter your password so that it connects.
There is the option of using a remote desktop app, this would display your actual desktop screen on the iPad and allow you to interact with the desktop right from the iPad.
I think the most convenient way would to somehow find an iPad app that does what you want. Have the patient records all stored on a remote server yet allow all connected iPad devices update the records.
What type of forms are they? are they PDF forms?
If they are PDF forms you could do the following. (forgive me I don't know the legalities of what is allowed to be used for security of patient information, this is just an example)
#1 setup FTP server at your location.
#2 load the FTP server with all of the forms and organize them how you would like into folders
#3 give access to the people allowed to access these forms by creating an FTP account for each person.
#4 users with access to these forms can then pull them up with an iPad app like iAnnotate PDF
#5 fill out any info on the forms and have patient sign document.
#6 save updated form directly to the FTP location where everything is stored.
#7 copies could also be printed right from the app if you need to give a copy to a patient.
This would keep the data secure by limiting access to those people with FTP accounts. The data would be transferred securely to the FTP server. The data would always remain within your network and never go out over the internet.